Morphing Planar Graph Drawings Optimally

  • Patrizio Angelini
  • Giordano Da Lozzo
  • Giuseppe Di Battista
  • Fabrizio Frati
  • Maurizio Patrignani
  • Vincenzo Roselli
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8572)

Abstract

We provide an algorithm for computing a planar morph between any two planar straight-line drawings of any n-vertex plane graph in O(n) morphing steps, thus improving upon the previously best known O(n2) upper bound. Furthermore, we prove that our algorithm is optimal, that is, we show that there exist two planar straight-line drawings Γs and Γt of an n-vertex plane graph G such that any planar morph between Γs and Γt requires Ω(n) morphing steps.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Patrizio Angelini
    • 1
  • Giordano Da Lozzo
    • 1
  • Giuseppe Di Battista
    • 1
  • Fabrizio Frati
    • 2
  • Maurizio Patrignani
    • 1
  • Vincenzo Roselli
    • 1
  1. 1.Dipartimento di IngegneriaRoma Tre UniversityItaly
  2. 2.School of Information TechnologiesThe University of SydneyAustralia

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